MOTION OF ELEMENT 

 -CONDUCTING EPOXy 



SMALL SPRING 



— ELECTRODES 



BOTTOh ELECTRODE 

 ATTACHED WITH 



CONDUCTING 



EPOXY 



POLARIZING DIRECTION- 



PIEZO-CERAMIC ELEMENT 



NODAL DIAMETERS 



FORCES EXERTED ON 

 POST BY DISC 



Fig. 2. Detailed schematic of mechanical resonator. 



ACCURACY CONSIDERATIONS 



The accuracy with which the frequency of this 

 type of resonator follows temperature changes 

 depends upon the Q of the resonator, for the fre- 

 quency must remain constant and he repeatable 

 for any one temperature. The higher the Q, the 

 less the frequency will he permitted to wander. 

 An approximate calculation (Fig. 3) shows that 

 if a maximum random phase variation of h'j degrees 

 is assumed in the amplifier circuit, an accuracy 

 of ±o.02°C requires a resonator Q of 4-5)000. 

 Most experimental resonators have had Q's of 

 45,000 and above when operating in a vacuum; in 

 fact, one was as high as 80,000. 



A wide band amplifier in the oscillator cir- 

 cuit with a resulting random phase shift much 

 less than 4-5 degrees would permit a lower Q 

 resonator to be used. However, this is not 

 feasible due to the presence of harmonics of the 

 described fundamental and many other modes that 

 can he excited and hence must be suppressed, 

 either by tuning the amplifier or filtering. 

 Either method will introduce some phase insta- 

 bility. A typical spectrum is shown in Fig. h. 

 This spectrum is shown from a slightly different 

 type of disc, having only one smaller post, but 

 the spectrum is typical. Most of these fre- 

 quencies belong to other modes of vibration. 



Only the second line at about 60 Kcps can be con- 

 sidered a legitimate overtone to the first line 

 with the characteristically high mechanical Q. 

 The fundamental frequency is used in the oscil- 

 lator circuit. The small circuit of Fig. 1 con- 

 tains two tuned circuits--a tank circuit tuned 

 to the fundamental frequency and a trap at the 

 first overtone. For laboratory measurements, 

 however, a low pass, sharp cut-off filter is used, 

 following an untuned amplifier (see Fig. 5)- 

 This method results in less change of phase with 

 different oscillation frequencies and greater 

 stability of phase at a given frequency. This 

 is shown by the fact that if all the inductors 

 in the filter circuit decrease their inductance 

 by 20$, the resulting phase shift through the 

 filter at a given frequency is only about 20 

 degrees. Not shown in Fig. 5 is a phase shift 

 circuit following the filter which is necessary 

 to obtain oscillations and will also be used in 

 the final unit to check periodically the resonator 

 Q. This will be done by introducing a known 

 phase shift and noting the resulting frequency 

 change . 



LABORATORY TESTS 



Laboratory tests have been conducted to check 

 the repeatability of the temperature sensor 



37 



